and, in particular, the topology induced on \(\mathbb {G}\)  by \(d\)  is the Euclidean topology. For \(p\in \mathbb {G}\)  and \(r > 0\) , \(\mathcal {U} (p,r)\)  will be the open ball associated with the distance \(d\) . Intrinsic \(t\) -dimensional spherical Hausdorff measure \(\mathcal {S}^{t}\)  on \(\mathbb {G}\) , \(t \ge 0\) , is obtained from \(d\) , following Carathéodory construction (see for instance [1]}).
